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Fractions and Unit (Part 1) by Daniel Mentrard

Fractions and Unit (Part 1) by Daniel Mentrard
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2020-03-06 16:17
FunctionTrigonometryCoordinate GeometryGeometric Construction
In collections The Fractions book The Fractions book
This example demonstrates the basic concepts and representation of fractions and unit lengths. It involves core mathematical concepts such as fractions, rectangles, rotation, linear equations, trigonometric functions, and similar triangles. GeoGebra commands and objects like Line, Point, Mod, Div, If, Translate, Dilate, Segment, Polygon, Sequence, Midpoint, and Vector are used in the construction. Suitable for middle school and above students to understand the connection between fractions and geometric transformations.

GeoGebra Commands & Parameters

  1. Line(A, xAxis) → q
  2. Point(q) → B
  3. Line(A, yAxis) → p
  4. Mod(Numerator, Denominator) → rs2
  5. Div(Numerator, Denominator) → Quot
  6. If(rs2 < nn, rs2, nn - 1) → result
  7. Point(q) → F
  8. Translate(D, Vector[(Quot * Vector[E, F])]) → D'
  9. Dilate(B, 1 / nn, A) → B'
  10. Point(p) → C
  11. Segment(A, B) → a
  12. Segment(A, C) → b
  13. Translate(D, Vector[A, B]) → D'_1
  14. Translate(D, Vector[A, C]) → D'_2
  15. Translate(D'_2, Vector[A, B]) → D''_1
  16. Segment(E, F) → c
  17. Polygon(D, D'_1, D''_1, D'_2) → poly2, d_1, d'_1, d'', d'
  18. Sequence(Polygon[Translate[D, Vector[(i * Vector[E, F])]], Translate[D'_1, Vector[(i * Vector[E, F])]], Translate[D''_1, Vector[(i * Vector[E, F])]], Translate[D'_2, Vector[(i * Vector[E, F])]]], i, 1, Quot - 1) → list1
  19. Translate(D', Vector[A, B]) → D''_2
  20. Translate(D', Vector[A, C]) → D''_3
  21. Translate(D''_3, Vector[A, B]) → D'''_1
  22. Segment(D', D''_2) → d
  23. Segment(D''_2, D'''_1) → e
  24. Segment(D''_3, D'''_1) → f
  25. Segment(D''_3, D') → g
  26. Sequence(Segment[Translate[D''_3, Vector[(i * Vector[A, B'])]], Translate[D', Vector[(i * Vector[A, B'])]]], i, 1, nn - 1) → list2
  27. Translate(D', Vector[(result * Vector[A, B'])]) → D''
  28. Translate(D'', Vector[A, C]) → D'''
  29. Polygon(D', D'', D''', D''_3) → poly3, d'_2, d''_1, d''', d''_3
  30. Segment(G, H) → i
  31. Segment(I, J) → h
  32. Sequence(Segment[Translate[D, Vector[(i * Vector[A, B'])]], Translate[D'_2, Vector[(i * Vector[A, B'])]]], i, 1, Denominator - 1) → list3
  33. Sequence(Sequence[Segment[Translate[Translate[D, Vector[(j * Vector[E, F])]], Vector[(i * Vector[A, B'])]], Translate[Translate[D'_2, Vector[(j * Vector[E, F])]], Vector[(i * Vector[A, B'])]]], i, 1, Denominator - 1], j, 1, Quot - 1) → list4
  34. Mod(Numerator, Denominator) → rest22
  35. Polygon(A, B, M, C) → poly1, a_1, b_1, m_1, c_1
  36. Sequence(Polygon[Translate[D, Vector[(i * Vector[E, F])]], Translate[D'_1, Vector[(i * Vector[E, F])]], Translate[D''_1, Vector[(i * Vector[E, F])]], Translate[D'_2, Vector[(i * Vector[E, F])]]], i, 1, Quot - 1) → liste1
  37. Sequence(Segment[Translate[D''_3, Vector[(i * Vector[A, B'])]], Translate[D', Vector[(i * Vector[A, B'])]]], i, 1, nn - 1) → liste2
  38. Sequence(Segment[Translate[D, Vector[(i * Vector[A, B'])]], Translate[D'_2, Vector[(i * Vector[A, B'])]]], i, 1, Denominator - 1) → liste3
  39. Sequence(Sequence[Segment[Translate[Translate[D, Vector[(j * Vector[E, F])]], Vector[(i * Vector[A, B'])]], Translate[Translate[D'_2, Vector[(j * Vector[E, F])]], Vector[(i * Vector[A, B'])]]], i, 1, Denominator - 1], j, 1, Quot - 1) → liste4
  40. Translate(A, Vector[B, F]) → A'
  41. Translate(B, Vector[B, F]) → B'_1
  42. Translate(M, Vector[B, F]) → M'
  43. Translate(C, Vector[B, F]) → C'
  44. Polygon(A', B'_1, M', C') → poly1', a', b'_1, m', c'
  45. Midpoint(N, O) → R
  46. Midpoint(P, Q) → S
  47. Vector(R, O) → u
  48. Vector(R, N) → v
  49. Vector(S, Q) → w
  50. Vector(S, P) → z
  51. Polygon(T, U, V, W) → poly4, t, u_1, v_1, w_1
  52. Polygon(D, D'_1, D''_1, D'_2) → poly5, d_2, d'_3, d''_2, d'_4
  53. Midpoint(B, A) → Z
  54. Vector(Z, B) → j
  55. Vector(Z, A) → l
  56. Midpoint(A, C) → A_1
  57. Vector(A_1, C) → m
  58. Vector(A_1, A) → n
  59. Midpoint(c') → B_1
  60. Midpoint(B, M) → C_1
  61. Midpoint(B_1, C_1) → D_1
  62. Vector(D_1, B_1) → r
  63. Vector(D_1, C_1) → s
  64. Line(E_1, F_1) → e_1
  65. Segment(G_1, H_1) → f_1
  66. Segment(I_1, J_1) → g_1

AI Drawing Prompt Reference

Draw a geometric figure involving unit lengths and fractions. Start by drawing the x-axis and y-axis, then create points and segments based on the numerator and denominator of a fraction. Use rotation and translation transformations to generate a series of similar rectangles, and finally, through translation and scaling, create multiple similar polygons to illustrate the relationship between fractions and geometric transformations.
The prompt above was compiled from the original drawing commands and is for reference only.